This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A066206 #32 Jan 16 2022 09:11:17
%S A066206 3,21,273,5187,150423,5565651,239322993,12684118629,773731236369,
%T A066206 54934917782199,4339858504793721,386247406926641169,
%U A066206 39010988099590758069,4174175726656211113383,471681857112151855812279,61790323281691893111408549,8588854936155173142485788311
%N A066206 a(n) = Product_{k=1..n} prime(2k), where prime(k) is the k-th prime.
%C A066206 From _Jon E. Schoenfield_, Jan 12 2022, Jan 15 2022: (Start)
%C A066206 Equivalently, a(n) is the product of the first n even-indexed primes.
%C A066206 Does r = prime(2n) * A066205(n)^2 / a(n)^2 approach a limit?
%C A066206 .
%C A066206 n A066205(n) a(n) prime(2n) r
%C A066206 ---- -------------------- -------------------- ---------- ----------
%C A066206 1 2 3 3 1.33333...
%C A066206 10 10156396926610 54934917782199 71 2.42683...
%C A066206 100 4.93803636802*10^255 1.00181029905*10^257 1223 2.97141...
%C A066206 10^3 1.5455035248*10^3740 1.2239433562*10^3742 17389 2.77263...
%C A066206 10^4 1.760119173*10^48693 5.011593123*10^48695 224737 2.77208...
%C A066206 10^5 3.26453781*10^596726 3.25976132*10^596729 2750159 2.75822...
%C A066206 10^6 3.2925831*10^7045939 1.1297886*10^7045943 32452843 2.75633...
%C A066206 10^7 8.085113*10^81117222 9.413111*10^81117226 373587883 2.75612...
%C A066206 10^8 5.34067*10^916830347 2.09048*10^916830352 4222234741 2.75575...
%C A066206 (End)
%H A066206 Harry J. Smith, <a href="/A066206/b066206.txt">Table of n, a(n) for n = 1..100</a>
%e A066206 a(3) = prime(2) * prime(4) * prime(6) = 3 * 7 * 13 = 273.
%p A066206 a:= proc(n) option remember;
%p A066206 `if`(n=0, 1, a(n-1)*ithprime(2*n))
%p A066206 end:
%p A066206 seq(a(n), n=1..17); # _Alois P. Heinz_, Jan 12 2022
%t A066206 FoldList[Times, Prime@ Range[2, 30, 2]] (* _Michael De Vlieger_, Sep 24 2017 *)
%o A066206 (PARI) { for (n=1, 100, p=1; for (k=1, n, p*=prime(2*k)); write("b066206.txt", n, " ", p) ) } \\ _Harry J. Smith_, Feb 05 2010
%o A066206 (PARI) a(n) = prod(k=1, n, prime(2*k)); \\ _Michel Marcus_, Jan 13 2022
%Y A066206 Cf. A000040, A002110, A066205.
%K A066206 nonn
%O A066206 1,1
%A A066206 _Leroy Quet_, Dec 16 2001